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%I #33 Dec 17 2023 10:26:22
%S 1,48,2305,110688,5315329,255246480,12257146369,588598272192,
%T 28264974211585,1357307360428272,65179018274768641,
%U 3129950184549323040,150302787876642274561,7217663768263378501968,346598163664518810369025,16643929519665166276215168
%N Denominators of continued fraction convergents to sqrt(577).
%C From _Michael A. Allen_, Dec 02 2023: (Start)
%C Also called the 48-metallonacci sequence; the g.f. 1/(1-k*x-x^2) gives the k-metallonacci sequence.
%C a(n) is the number of tilings of an n-board (a board with dimensions n X 1) using unit squares and dominoes (with dimensions 2 X 1) if there are 48 kinds of squares available. (End)
%H Vincenzo Librandi, <a href="/A042105/b042105.txt">Table of n, a(n) for n = 0..200</a>
%H Michael A. Allen and Kenneth Edwards, <a href="https://www.fq.math.ca/Papers1/60-5/allen.pdf">Fence tiling derived identities involving the metallonacci numbers squared or cubed</a>, Fib. Q. 60:5 (2022) 5-17.
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (48,1).
%F a(n) = F(n, 48), the n-th Fibonacci polynomial evaluated at x=48. - _T. D. Noe_, Jan 19 2006
%F From _Philippe Deléham_, Nov 23 2008: (Start)
%F a(n) = 48*a(n-1) + a(n-2), n>1; a(0)=1, a(1)=48.
%F G.f.: 1/(1 - 48*x - x^2). (End)
%t a=0;lst={};s=0;Do[a=s-(a-1);AppendTo[lst,a];s+=a*48,{n,3*4!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 03 2009 *)
%t Denominator[Convergents[Sqrt[577], 30]] (* _Vincenzo Librandi_, Jan 14 2014 *)
%t LinearRecurrence[{48,1},{1,48},20] (* _Harvey P. Dale_, Aug 21 2019 *)
%Y Cf. A042104, A040552.
%Y Row n=48 of A073133, A172236 and A352361 and column k=48 of A157103.
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_
%E Additional term from _Colin Barker_, Dec 01 2013
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